Rewrite the function y = x2 - 6x + 14

Answers

Answer 1

Answer: y = x² - 6x + 14

rewrite in vertex form:

y - 14 = x² - 6x

perfect square trinomial.
x² ⇒ x * x
-6x ⇒ -6x / 2 = -3x
-3² = 9

(x - 3)² ⇒ (x-3)(x-3) ⇒ x(x-3) -3(x-3) = x² - 3x - 3x + 9 = x² - 6x + 9

y - 14 + 9 = (x-3)²
y -5 = (x-3)²
y = (x-3)² + 5

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What is the length of the hypotenuse, x, if (12, 35, x) is a Pythagorean triple?

Answers

Answer:

x = 37

Step-by-step explanation:

Lets take 12 as base (b) and 35 as perpendicular (p)

The hypotenuse (h) = x = ?

We know by using Pythagoras theorem

$h^(2) =p^(2) +b^(2)$

$h^(2) =35^(2) +12 ^(2)$

$h^(2) = 1225 + 144\nh^(2)= 1369$

h = $√(1369)$

Therefore h = 37

Hope it was helpful:)

LOTS OF POINTS, THANKS, AND BEST ANSWER!!The dimensions of a conical funnel are shown below:

A conical funnel is shown with the height of the cone as 8 inches and the radius of the base as 3 inches.

Nisha closes the nozzle of the funnel and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 15 cubic inches per minute, how long will it take for all the liquid to pass through the nozzle? (Use π = 3.14.)

Answers

The volume of the conical funnel is given by V = 1/3 pi (r^2)h; where pi = 3.14, r = 3 and h = 8. Therefore, V = 1/3 pi (3^2) x 8 = 24pi = 75.36. Now, the liquid drips at the rate of 15 cubic inches per minute. Thus it will take it 75.36 / 15 = 5.024 minutes forthe water to pass through the nozzle.

Answer:

Your answer would be B: (5.02) minutes

Step-by-step explanation:

150 adults complete a survey.80 are women.
Write the ratio

in its simplest form.

Answers

150: 80 = 1 7/8 hope u have a blessed day

Answer:

7:8

Step-by-step explanation:

150 adults complete a survey.

80 are women

therefore 70 are male (150-80)

the ration would be 7:8

Why does the term angle need to be defined prior to defining perpendicular lines?

Answers

Answer:

Perpendicular means "at right angles".

A line meeting another line at a right angle, or 90° is said to be perpendicular to it.

This is why we need to know what are angles first.

Angles are defined as the space between two intersecting lines close to the point where they meet.

So, when we say perpendicular lines meet at 90° angles, we must know the definition of angles.

Perpendicular lines are two or more lines that intersect at a 90-degree angle, like the two lines drawn on this graph, and the x and y axes that orient them.

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